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Observing an astronaut falling into a black hole 
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#1
Apr2107, 03:27 PM

P: 11

From what I understand, if an outside observer was to witness an astronaut falling into a black hole, relativity dictates that we would see him approach the black hole slower and slower until he ultimately "freezes" in our relative time due to time dilation. My question is, would we actually observe a frozen astronaut in space from our perspective (as in a photographic snapshot)? Doesn't the light become so redshifted that the astronaut's image would appear redder until ultimately fading away?



#2
Apr2107, 04:08 PM

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P: 6,040

You are right about the light of his image being redshifted, even though he is frozen in space.



#3
Apr2107, 08:14 PM

P: 11

So my question is, would the light be so redshifted that we would not even be able to visibly see an image of the astronaut?



#4
Apr2107, 09:01 PM

PF Gold
P: 247

Observing an astronaut falling into a black hole
A finite number of photons is emitted before the astronaut crosses the horizon. In the continuum approximation, the light intensity decreases exponentially ∝ exp(t/3√3 M) so that it will almost instantly completely disappear from sight.



#5
Apr2107, 09:16 PM

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#6
Apr2107, 10:48 PM

Emeritus
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P: 7,599

Eventually there will be a last visible photon, as the laser beam quickly redshifts below the visible region. In fact, given any nonzero frequency, there will be some time at which no photons are emitted above that frequency. In the book I mentioned, there will be a time of last emission of 4km radio waves, the lowest frequency that the monitoring observer can detect. I believe this is also discussed in MTW's textbook "Gravitation", but I couldn't find the exact page. As Thorne is one of the authors of this book, I would expect that it would be the same answer as found in the more readilly accessible "Black Holes & Time Warps". 


#7
Apr2207, 12:40 AM

P: 2,043

Also, just because photons are no longer received by the observer does not mean they were not emitted by the astronaut, it just means that the spacetime paths of the photons no longer have an intersection point with the spacetime path of the observer, in fact after the astronaut passes the event horizon all the photon paths head for the singularity. 


#8
Apr2207, 01:52 AM

PF Gold
P: 247




#9
Apr2307, 10:39 AM

Sci Advisor
P: 2,340

See http://math.ucr.edu/home/baez/RelWWW/HTML/reading.html for the full bibliographic citations. Enjoy! 


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